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P-Sensitive Functions and Localizations

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  • Johannes Langner
  • Gregor Svindland

Abstract

This paper assumes a robust stochastic model where a set $\mathcal{P}$ of probability measures replaces the single probability measure of dominated models. We introduce and study $\mathcal{P}$-sensitive functions defined on robust function spaces of random variables. We show that $\mathcal{P}$-sensitive functions are precisely those that admit a representation via so-called functional localization. The theory is applied to solving robust optimization problems, to convex risk measures, and to the study of no arbitrage in robust one-period financial models.

Suggested Citation

  • Johannes Langner & Gregor Svindland, 2026. "P-Sensitive Functions and Localizations," Papers 2601.19511, arXiv.org.
    • Handle: RePEc:arx:papers:2601.19511
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    References listed on IDEAS

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